Question

The world’s two highest dams are both in Tajikistan. The Rogun dam is 35 meters taller than the Nurek dam. Together they are 635 meters tall. Find the height of the Nurek dam

Answer 1

Answer: Rogun dam is 335m tall and Nurek dam is 300m tall

Step-by-step explanation:

I will use $r$ to represent the height of the Rogun dam and $n$ to represent the height of the Nurek dam.

The system of equations is as follows:

$r+n=635$

$r-n=35$

From the second equation, we can rearange it to be:

$r=35+n$

Then take this new value of $r$ and plug it into our first equation to find $n$

$(35+n)+n=635$

$35+2n=635$

$2n=600$

$n=300$

This means that the Nurek dam is 300m tall, and the Rogun dam is 335m tall, found by pluggin the value into our first equation:

$r+300=635$

$r=335$